On Mon, Aug 12, 2013 at 12:38 PM, Auguste Pop <auguste@gm=
ail.com> wrote:

In order to illustrate how large the error is, I have inc=
luded a two graphs. These graphs show the absolute error from a point on th=
e bezier curve to the circle. We get the graphs with the assumption that we=
are approximating a pi/4(45 degrees) arc on an unit circle.

--001a11c31fd438b42b04e3b9f208--On Mon, A= ug 12, 2013 at 12:21 AM, Jasper van de Gronde <th.v.d.gronde@hccnet.= nl> wrote:

On 2013-08-10 07:14, Auguste Pop wrote:

> ...

> Should I file a bug report? Please comment.It is not entirely clear to me in what way the approximation is /wron= g/.

It is impossible to represent a circular arc using a B=C3=A9zier curve, and=

there is thus not one best approximation. In my experience the curves

look pretty decent, if you have an example where the approximation is

clearly of very bad quality, that would be interesting.

As for the inconsistency, that could indeed be considered a bug.

(Although as long as both approximations are of sufficient quality, I

wouldn't be too worried.)I said = the approximation is "wrong" because there's no literature or= resource that I am aware of comes up with this solution. I know an circula= r arc can not be represented by a cubic bezier curve losslessly. But with a= certain criteria, there's certainly a "best" approximation. = The "best" approximation may be very difficult to calculate, so w= e will finally use some "good" answers. The traditional approxima= tion which puts the middle point of bezier curve on the arc is one of the &= quot;good" answers. In any case, the approximation used by "Edit = path by nodes" is not "good" nor "best".Of course, this can not be "wrong" as the err= or is still relatively slow to human eyes. When inkscape is treated as a de= sign tool, this behavior is acceptable. But as a computer program, it is us= ing the "wrong" equation mathematically.Best regards,

=
=C2=A0

The tradito=
nal.png shows the error when using the traditional method. And the comparis=
on.png shows the both errors from the traditional method and the method i t=
hink "wrong". Although the method in question still gives a relat=
ively small error (about one thousandth), it is significantly worse than th=
e traditional method (max error on 10^-6 order).

Best regard=
s,